114 



REPORT 1873. 



T. XXXII. Functiones Jiypcrlolicce circularibus analogs. Q, q being a 

 rectangular hyperbola, centre C, P C Q is tlie so-called angulus imnscendens 

 = say, 5 C Q the angulus communis =\{/ say; jj ^ is the hyperbolic sine, 

 C p the hyperbolic cosine, and C g Q the sector ; so that if the hyperbola be 

 .^■'^ — ?/- = ], .r=sec and ?/=tan <p. 



Tlie argnment is 0, and proceeds from 0° to 90° at intervals of 1° ; and 

 the table gives the sector, y, x, log y, log .r, tan i^, log tan i// and ;//, all ex- 

 cept the last to 7 places, and the last to one decimal of a second. 



T. XXXV. & XXXYI. Squares and cubes of numbers from 1 to 



T. XXXVII. 



^+l)(^+2) 

 1".2:3 



Figurato 



numbers 

 .(a:-fll 



1.2.3... 12 



(first 12 series), viz. x, 

 from a'=l to 30. 



T. XL. First 11 powers of -01, -02, -03. . .1-00, to 8 places. 



1000. 



x{x^^) 



their 



T. XLIV. Coefficients of the first 16 terms in (l-j-.r)^ and (l + .r)''^, 

 accurate values being given as decimals. 



Besides the above, T. XIX. gives sin 3°, G° . . .89° in radicals, and T. XLII. 

 the first 6 or 9 convergents to \/2, >^3, i^5...>i/12 as vulgar fi-actions. 

 The other tables contain formulte &c. 



The work is edited by Felkel, who has prefixed a Pra'fatlo Interpretis of 

 xi pp., giving a description of his (Felkel's) tables of divisors &c. ; and there 

 is also added at the end an account of his proposed scheme of tables in rela- 

 tion to the theory of numbers. About Felkel, see Felkel, 1776, § 3, art. 8. 



The titlepage states that this is a translation from a German edition. The 



original was entitled 



' Zusatze zu den logarithmischen tind trigonometrischcn 



Tabellen," and was published in 1770 ; or, at all events, De Morgan's descrip- 

 tion of the contents of this latter work, which we have not seen, agrees, 

 as far as it goes, almost entirely with the ' Supplementa ' &c., which De Morgan 

 had heard of, but not seen. The introduction to the latter shows signs of 

 having been amplified by Felkel. 



Lax, 1821. T. XIV. Proportional logarithms, viz. log 10800" — log .r 

 from .r=0" to 07=10800" (=3°) at intervals of 1" (the arguments being 

 expressed in degrees, minutes, and seconds), to five places. On the first page, 

 however, which extends to 10', only two, three, or four places arc given cor- 

 rectly, the number being filled up to five by adding ciphers ; facing 0° 0' 0" 

 there is given 4-88. . instead of — oo . 



T. XVII. Xatural versed, suversed, coversed, and sucoversed sines, viz. 

 1 — cos x and 1 + cos .r for every minute of the quadrant, to six places, with 

 proportional parts for 1", 2".. .60", so that the tabular results can be taken 

 out very easily to seconds. It may be observed that of tbe double columna 



